Circle And System Of Circles Question 135
Question: The equations of the tangents to the circle $ x^{2}+y^{2}-6x+4y=12 $ which are parallel to the straight line $ 4x+3y+5=0 $ , are
[ISM Dhanbad 1973; MP PET 1991]
Options:
A) $ 3x-4y-19=0,3x-4y+31=0 $
B) $ 4x+3y-19=0,4x+3y+31=0 $
C) $ 4x+3y+19=0,4x+3y-31=0 $
D) $ 3x-4y+19=0,3x-4y+31=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
Let equation of tangent be $ 4x+3y+k=0 $ , then $ \sqrt{9+4+12}=| \frac{4(3)+3(-2)+k}{\sqrt{16+9}} | $
$ \Rightarrow 6+k=\pm 25\Rightarrow k=19 $ and $ -31 $ .
Hence the tangents are $ 4x+3y+19=0 $ and $ 4x+3y-31=0 $ .
BETA
